I'm working through revision questions at the moment and we are asked to compute the price of an American call option.

Suppose that $dS_t = \sigma S_t dW^*_t, S_0 >0$

Let $0<U<T$ be fixed dates and let $K>0$ be a constant. Consider the American call option with expiration date $T$ and payoff process $(X_t)_{t\in[0,T]}$ given by the following expressions:

$X_t = g_1(S_t,t) = (S_t-K)^+ , \forall t \in [0,U]$


$X_t = g_2(S_t,t) = (S_t-S_U)^+ , \forall t \in (U,T]$

Find the arbitrage price of the option at time $t\in [0,T]$

We know that in time $t \in (U,T]$ the price is a European call with strike $S_U$, and the price at time $U$ is max$(C_u(K), C_u(S_u))$ (I think).


closed as unclear what you're asking by SRKX Jun 18 '15 at 4:33

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  • $\begingroup$ "Analyze the price" is too vague to be answered properly here. What are you looking to express? Please rephrased you title as a question and make it specific in the description; we will then reopen the question. $\endgroup$ – SRKX Jun 18 '15 at 4:33